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Author Topic: The reason that spinning tops rise  (Read 751 times)

Iacopo

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The reason that spinning tops rise
« on: July 09, 2018, 04:05:13 PM »

I have made a video trying to explain the reason that spinning tops tend to rise while spinning, if their rotational speed is high enough.

https://www.youtube.com/watch?v=BBRNMmSwyQs


« Last Edit: July 10, 2018, 10:38:13 AM by Iacopo »
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Iacopo

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Re: The reason that spinning tops rise
« Reply #1 on: July 10, 2018, 10:41:40 AM »

I have corrected some editing problems in the video and uploaded it again.  Now it works fine.  :)
Maybe I should buy some better editing software.
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Iacopo

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Re: The reason that spinning tops rise
« Reply #2 on: July 10, 2018, 01:52:55 PM »

Spinning tops are very complicated.
I have not expressed this in the video, but the slowing down of the top, due to air drag and tip frictions, has certainly some effect on the rising torque.  I have to think more about it.  But I have some ideas that I will expose here. 
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Jeremy McCreary

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Re: The reason that spinning tops rise
« Reply #3 on: July 10, 2018, 02:17:40 PM »

Eager to study this new video as soon as I'm able to pry my mind away from the Limbo mystery. Your videos never disappoint, and I look forward to seeing your take on this important and still controversial subject.

Spinning tops are very complicated.

That's putting it mildly, my friend. It's also very counterintuitive. I mean, what could be simpler than a finger top??

Average glaze-over time observed when trying to convince folks in my LEGO group that it takes a lot of subtle engineering to coax long, smooth spins or specific behaviors out of LEGO tops: 2 seconds, tops. ::)
« Last Edit: July 10, 2018, 02:20:12 PM by Jeremy McCreary »
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Playing with the physical world through LEGO

Iacopo

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Re: The reason that spinning tops rise
« Reply #4 on: July 11, 2018, 09:31:39 AM »

still controversial subject.

Yes, I have read different things, (not many), and it seems like there are different ideas about this subject.
It is a long time that I wanted to make this video, and it is exactly because of those contradictions that I hesitated, but, by the time, I have become more confident with my actual ideas, so I made the video.  I think there shouldn't be big errors in it, but the subject is not simple, then I have not studied physics, so criticism will be well accepted. 
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Iacopo

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Re: The reason that spinning tops rise
« Reply #5 on: July 11, 2018, 10:47:40 AM »

Some time ago Ta0 suggested me to read a book, Spinning tops by JOHN PERRY, (it is a nice book that can be found for free on gutenberg.org).

In this book there is an explanation of the rising top, which I partially included in the video, (from 5:20).

The explanation given by Perry is that the peg rolling on the table hurries on the precession, and, doing so, the top rises in opposition to gravity.
My explanation is partly different from that given by Perry, because I believe that the peg rolling on the table by itself is not enough for to cause a push in the direction of to hurry on the precession;
 
a torque is needed, acting on the axis of rotation, for to make the top rise.
A torque is a couple of forces, (two fingers are needed for to turn a key), or a force and a resistance.

In the case of the spinning top, one force is the peg rolling on the table and pushing the top in one direction, but which is the other force/resistance ? 
In the sample in my video, it is inertia at the center of mass, which, temporarily, for a short while, opposes the push of the tip, so the top can rise a bit.
This could happen at the beginning of a spin, when the top is already spinning but it is not moving yet along the table.

But, as the top moves along the precession trajectory, the tip and the center of mass go hand in hand, with the same angular speeds, so there isn't anymore an inertial resistance, nor a torque consequently, to make the top rise.

In gyroscopes it is sufficient to push a gimbal for to hurry on the precession;
but this is different, because, while pushing the gimbal, we are indeed applying a torque to the rotor of the gyroscope, not a simple force;
in fact the center of mass of the rotor of a gyroscope is held in a steady position by the gimbals.
A torque is needed for to make a top rise.

Since the center of mass of a top is not steady but it is free to move where it wants, I believe that the effect of the rolling tip on the table is not that of to make the top rise, but only that of to move the center of mass and the whole top along a circular trajectory on the table.   
 
 
« Last Edit: July 11, 2018, 01:26:34 PM by Iacopo »
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Jeremy McCreary

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Re: The reason that spinning tops rise
« Reply #6 on: July 11, 2018, 01:47:58 PM »

Thanks for the explanation! Once I'm done delving into the Limbo mystery, I'll return to this complex subject.

Meanwhile, I'll email you a very readable PDF article on it by physicist Rod Cross, who sides strongly with the rolling resistance camp. You'll be interested in his diagram of the forces acting on the tip when it's rolling without slip.

The articles I have from the friction camp are very math-heavy (in, part, because friction is easier to quantify), but I'll try to find one for you. Rolling resistance and friction are =not= the same thing.

Complicating the whole matter are tops that clearly roll =with= slip for a time after a strenuous spin-up -- like a dragster spinning its wheels. I've made many of these. Eventually, pure rolling sets in, but they can rise during the roll+slip phase, too.

I've also made tops that =never= rise -- at least not at attainable launch speeds. Most of these have high CMs and TMI/AMI ratios and short spin times.

Some useful terminology: The pair of torques contact forces present when your fingers drive the stem cooperate with equal magnitude and distance from a shared axis. In this special but fairly common situation, "couple" can refer to either the special force pair or the special torque it produces.
« Last Edit: July 11, 2018, 05:22:17 PM by Jeremy McCreary »
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Iacopo

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Re: The reason that spinning tops rise
« Reply #7 on: July 11, 2018, 04:27:16 PM »

Thank you, Jeremy.  I remember you already posted something written by Cross, long time ago, but if you have something I could read, I will read it gladly. 
In italian we say "coppia" (literaly "couple") to say "torque". 
In english, is "couple" also a synonymous of "torque" ?
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Jeremy McCreary

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Re: The reason that spinning tops rise
« Reply #8 on: July 11, 2018, 05:07:13 PM »

In english, is "couple" also a synonymous of "torque" ?
In italian we say "coppia" (literaly "couple") to say "torque".  In english, is "couple" also a synonymous of "torque" ?

Sorry, had to correct that last paragraph in my last post.

In English, "couple" usually refers to a special kind of torque arising from a pair of forces in a special but common scenario. But you'll also see "couple" used for the special force pair producing the special torque.
« Last Edit: July 11, 2018, 05:20:09 PM by Jeremy McCreary »
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Iacopo

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Re: The reason that spinning tops rise
« Reply #9 on: July 12, 2018, 12:21:37 PM »

I'll email you a very readable PDF article on it by physicist Rod Cross, who sides strongly with the rolling resistance camp.

I think you refer to:

The rise and fall of spinning tops. Available from: https://www.researchgate.net/publication/258757498_The_rise_and_fall_of_spinning_tops

I read it long time ago, (it was you that reported it in this forum, so thanks !), now I have read it again;
I believe quite strongly that he is right, rolling resistance is responsible for the rising top, like I too exposed in my video, (at least normal tops, not the tippe top which I have not studied and I don't know how it works yet).
 
Also, I found some empirical evidence of this to be true:

In fact tops with a teflon peg rise very fast, and this cannot be due to sliding friction because sliding friction of teflon is very low, as demonstrated by very long spin times of tops with a teflon tip, so the cause must be another one.
I have not found data of the coefficient of rolling resistance of teflon, but I found data telling that plastic materials have generally higher
rolling resistance than metals, so rolling resistance can be the cause.

Also, it is obvious that the torque of rolling resistance is in the correct direction for making tops rise.
I can't say the same for sliding friction, but I explain this better in the video.

It is also interesting to note that, generally, using a lubricant in the spinning surface, makes the top to spin longer, but, at the same time, makes the top to rise faster.
If sliding friction was responsible for the rising top, how could be possible that with less sliding friction the top rises faster ?
« Last Edit: July 13, 2018, 12:37:25 PM by Iacopo »
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Iacopo

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Re: The reason that spinning tops rise
« Reply #10 on: July 13, 2018, 12:28:04 PM »

Complicating the whole matter are tops that clearly roll =with= slip for a time after a strenuous spin-up -- like a dragster spinning its wheels. I've made many of these. Eventually, pure rolling sets in, but they can rise during the roll+slip phase, too.

My tops rarely slip, maybe because they are relatively heavy, with little or pointed tips, and they are spun with fingers, so they never spin really very fast.

But I have a case of a slipping top, and a little mistery solved;

this is the case of my top with its center of mass at the tip, this top has not precession.
When it is spun in tilted position, it stays in that tilted position without precessing, and, slowly, it rises, with the stem going directly to the vertical position, without precessing.

It was argued that the top couldn't rise if there was not precession, so this was a little mistery.

But, if rolling resistance is considered, the explanation becomes easy;

In the drawing below, the top spins in tilted position, it does not precess, so it stays in that position;
the tip is pointed, but not really sharp, so it behaves like a tiny ball tip.
The tip acts like a drive wheel and pushes the top towards the left.
Since there is not precession, the top continues to go to left, and the tip, rolling, climbs on the side of the spinning surface;
here the tip starts slipping and remains in that position, slipping continuously.



The torque due to the contact point shifted forward from the center of mass, (red arrows), is the same of that of a ball rolling uphill, this torque makes the top rise.

« Last Edit: July 14, 2018, 08:20:09 AM by Iacopo »
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Jeremy McCreary

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Re: The reason that spinning tops rise
« Reply #11 on: July 13, 2018, 06:59:41 PM »

I  think you refer to:
The rise and fall of spinning tops. Available from: https://www.researchgate.net/publication/258757498_The_rise_and_fall_of_spinning_tops

I read it long time ago, (it was you that reported it in this forum, so thanks !), now I have read it again;
I believe quite strongly that he is right, rolling resistance is responsible for the rising top, like I too exposed in my video, (at least normal tops, not the tippe top which I have not studied and I don't know how it works yet).

Yes, that's the one. He may well be right, but the fact that the topic remains controversial in the literature gives me pause. Usually means that both sides are wrong to some extent.

Also, I found some empirical evidence of this to be true...

Very interesting and important observations. Will comment shortly.

I have not found data of the coefficient of rolling resistance of teflon, but I found data telling that plastic materials have generally higher
rolling resistance than metals, so rolling resistance can be the cause.

The bad news: Unlike sliding friction, rolling resistance may not be quantifiable with a simple coefficient depending only on materials and independent of speed. Tip and ground deformation at the contact patch is clearly important, however tiny, and nothing about that is simple.
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Jeremy McCreary

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Re: The reason that spinning tops rise
« Reply #12 on: July 13, 2018, 07:11:42 PM »

Excellent, Iacopo! The observations in your last 2 posts aren't just interesting and careful and clever. They're also key: They must fit well in any successful general theory of the rising of tops.

Your observations also show just how complex the phenomenon really is. In cases like this, simple, intuitive explanations -- especially of the "it's just one thing" variety -- tend to fail on closer inspection. As everyone here knows, rotation complicates everything all by itelf. Ditto for aerodynamics. And ditto for the entire range of poorly understood contact processes where the tip and ground meet.

If I may get a little philosophical in a physical sense...

In the playground we call a spinning top, inertial, gravitational, aerodynamic, and tip-related processes come together, continually overprinting each other in ways that seldom fail to entertain. The players in the game at pretty much every step include
o overall size
o detailed shape
o density distribution
o total mass
o aerodynamic properties of the wetted surface -- especially surface texture and any streamlining or lack thereof
o tip configuration and materials
o ground configuration and materials
o air density
o lauch speed
o physical details of the release
 
Much of the inherent nonlinearity in top behavior resides in the fact that player interactions both determine and react to the actual spin vs. time curve followed.

To make matters worse, many of the physical processes involved are understudied and/or poorly understood under applicable conditions. After years of seaching the literature, I have yet to find even an attempt to predict the detailed behavior of a real-world top contending with =both= the air and the ground at the same time. For such a seemingly "simple" system, that fact alone speaks volumes.

In short, there's a whole lotta complexity going on -- even in the best-controlled of situations. It's easy to get frustrated or put off by it, and some will be tempted to ignore it. Heck, I get frustrated, too.

But top fanciers certainly enjoy watching the complexity unfold after a twirl (though they may not think of it in those terms). To this habitual top engineer and builder, grappling with the complexity adds way more fun than cussing -- and I suspect it's the same for you.

After all, some very cool stuff goes on here, and it's not just theoretical.
« Last Edit: July 13, 2018, 07:25:47 PM by Jeremy McCreary »
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Iacopo

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Re: The reason that spinning tops rise
« Reply #13 on: July 14, 2018, 10:18:50 AM »

the fact that the topic remains controversial in the literature gives me pause. Usually means that both sides are wrong to some extent.

Jeremy, do you know if those who disagree about rolling resistance as the cause of the rising top, think the same as Perry, that the cause is the peg that, rolling on the table, " wants to roll the top faster than the precession lets it roll, so that it hurries on the precession, and therefore the top rises" ?  Is this the common given explanation by them ?

I see a big problem with this explanation given by Perry, because there is not a resistance of whatever kind at the center of mass, to the "push" of the peg rolling on the table, so there can't be a rising torque.

In the sample given by Perry of how to prolong the spin time of a top supported on a hand, by dexterously helping the precession, by giving the hand a circling motion, what makes the top to rise is, again, a torque, not a simple push;
in fact the hand (and the peg) can be moved horizontally with accelerations and decelerations, which find an inertial resistance in the CM of the top, so a torque is being applied in this case.     

« Last Edit: July 15, 2018, 03:36:34 PM by Iacopo »
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Iacopo

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Re: The reason that spinning tops rise
« Reply #14 on: July 14, 2018, 10:57:31 AM »

Unlike sliding friction, rolling resistance may not be quantifiable with a simple coefficient depending only on materials and independent of speed. Tip and ground deformation at the contact patch is clearly important, however tiny, and nothing about that is simple.

In fact I didn't find many data about coefficients of rolling resistance, and the ones I found were a bit dissimilar, but plastics have constantly a higher coefficient that that of more rigid materials, and, anyway, it makes sense to me that softer materials with slower resilience have higher rolling resistance.  I couldn't find a better explanation for the fast rising of tops with a teflon tip.
---------------------------------------------------

If rolling resistance is dependent on speed, this can explain why larger ball tips make the top to rise faster;

Rolling resistance is said to be higher in littler wheels, (and balls, I suppose);
if so, the tops rising faster should have littler ball tips, not larger ones.

But if speed is considered, we see that tops with larger tips make larger circles on the spinning surface, at a higher speed;
this could explain the apparent paradox.

« Last Edit: July 15, 2018, 03:35:10 PM by Iacopo »
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